Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 11 - 2019

(i) The device used to reduce a.c. voltage is a transformer. It works on the principle of electromagnetic induction to step down or step up the voltage as needed.

(ii) To convert current from a.c. to d.c., the device used is a rectifier. This component transforms alternating current into direct current by allowing only one direction of current to pass through.

Hooke's law states that the restoring force ($F$) in a spring is directly proportional to the displacement ($x$) from its equilibrium position. This relationship can be expressed mathematically as:

$F = -kx$

Where:

• $F$ is the restoring force
• $k$ is the spring constant
• $x$ is the displacement.

To calculate the force exerted by the wall on the ball, we first find the change in momentum ($riangle p$) of the ball.

1. Convert mass from grams to kilograms: $m = 110 ext{ g} = 0.110 ext{ kg}$

2. Determine initial and final momentum:

   • Initial momentum ($p_i$) = $mv = 0.110 imes 4 = 0.44 ext{ kg m/s}$
   • Final momentum ($p_f$) = $mv = 0.110 imes (-4) = -0.44 ext{ kg m/s}$

3. Calculate the change in momentum: $riangle p = p_f - p_i = -0.44 - 0.44 = -0.88 ext{ kg m/s}$

4. Calculate the force ($F$) using the formula: F = rac{ riangle p}{ riangle t} = rac{-0.88}{0.2} = -4.4 ext{ N} The negative sign indicates direction; the magnitude of the force exerted by the wall is 4.4 N.

To show the formation of an upright image using a magnifying glass, draw a ray diagram illustrating the following:

• An object placed just inside the focal point of the converging lens.
• Two rays: one ray coming parallel to the principal axis, refracted through the focal point; another ray passing through the center of the lens.
• The rays will diverge after passing through the lens, and the extension of the rays will meet on the same side as the object to form an upright virtual image.

The nuclear equation for the fission of plutonium-239 upon the collision with a neutron can be represented as follows:

$^{239}_{94} ext{Pu} + ^1_0n \rightarrow ^{134}_{54} ext{Xe} + ^{103}_{40} ext{Zr} + 3 ext{n}$

To calculate the energy released in the fission reaction, we first need to find the mass defect.

1. Calculate the mass before and after the reaction:

   • Mass before = Mass of plutonium-239 + Mass of neutron

   • Mass after = Mass of xenon-134 + Mass of zirconium-103 + Mass of neutrons produced

     Mass before: $= 239.052163 u + 1.008665 u = 240.060828 u$

     Mass after: $= 133.903595 u + 102.926599 u + 3 imes 1.008665 u = 239.855524 u$

2. Calculate the mass defect: $\Delta m = 240.060828 u - 239.855524 u = 0.205304 u$

3. Convert mass defect to energy using Einstein’s mass-energy equivalence formula, $E = mc^2$:

   We know that: $E = 0.205304 u \times 931.5 \text{ MeV/u} = 191.062 ext{ MeV}$ Therefore, the energy released in the reaction is approximately 191.062 MeV.

The energy released during the fission process is primarily in the form of kinetic energy of the fission fragments and the emitted neutrons. Additionally, some energy is released as heat, which can subsequently be harnessed for power generation.